I don't have a problem with transgenderism, when done properly. What I mean by that is this:

I have two close transgender friends.

One of them treats their gender as an aspect of their identity. Chances are if someone said "Hey do you know xxxxxx?", someone would say "I think so. Isn't he that guy who, plays guitar/does sound engineering/likes dancing etc"
One of them lets their gender consume their whole identity. 90% of what they post online is about the fact they are non binary in gender. One of my close friends is friends with this person on facebook and agrees with me. Based on what they post on facebook, this friend of mine can determine nothing about them other than the fact that they are transgender. Chances are if someone said "Hey do you know xxxx?", someone would say "Are they that transgender person?" as opposed to "I think so, they like Pokemon/is a hairdresser/into gothic clothing aren't they?". I mean, I would rather refer to me as "that musician guy" or "that guy who likes pokemon" instead of "That Cysgender guy." This leads into my next point.

One of them has never even mentioned being transgender. Within weeks of knowing him, myself and my classmates simply knew. He became 'one of the guys'. And we all accepted that.
The other tends to force their gender identity down other peoples throats, and honestly, I just find it irritating. I find my religion to be a massive aspect of my identity, but I don't shove it down people throats. All I ask is that others don't shove their beliefs down mine.

One of them doesn't expect everyone else to change for him. He makes people want to change by being a really nice person. People would want to change to stay friends with him.
The other expects the world to change for them, in a sense that if anyone even accidentally slips up with pronouns, they will bite their head off. I guess that I have always gone by the mindset "Don't be an effort." I feel like my presence shouldn't make people work any harder, and vice versa.

One of them is an example of someone treating their gender identity maturely.
The other isn't.

Essentially, I have no problem with transgenderism, as long as they are mature about it.

On a slightly related note, the whole Caitlyn Jenner things irks me, but not because of the gender thing. More the fact that the media are trying to portray a 65 year old as a sexualized 25 year old. I dunno, I guess I just find it slightly perverted. I guess that they wouldn't do that with a 65 year old cysgender woman, so why do it with Caitlyn. But I guess that is just the media/Kardashians doing what they do best.